Hydrogeology



Theis type curve solution Reading: Fetter, pp. 166-177

Non steady-state flow to a fully confined well

Graphical solutions to flow equations: Theis type curve method, (Cooper) Jacob time drawdown and distance drawdown methods

Introduction:

- Previous emphasis: Predicting drawdown based on known aquifer parameters.

Examples:

- You get a call from a client, they want to know why their well went dry

- You need to design a de-watering project

- You need to predict drawdown from multiple wells or aquifers with hydraulic boundaries

- Now: We will look at another aspect of flow to wells: making estimates of aquifer parameters (T, K, S) based on field data, aquifer tests

Define: pump test vs. pumping test (aquifer test)

A pump test tests a pump

An aquifer test tests an aquifer

- 2 basic approaches to the solution:

- Use type curves that represent graphical solutions for our flow equations

- Use straight line graphical solutions

- The objective in both methods: find T, K and S

Point to remember: all of these methods are for non-equilibrium flow (non-steady-state)

- Cone of depression is still expanding

I) Non equilibrium flow in a confined aquifer: Theis method

- Take the Theis equation, solve for T:

ho-h = Q W(u)

4πT

becomes:

T = Q W(u)

4π (ho -h)

- Also need to rearrange our well function solution equation, solve for S:

u = r2 S becomes S = 4 T t u

(4Tt) r2

- note: time is in DAYS here (it will be in minutes below)

- So: how do we get these numbers from an aquifer test?

- Answer: the well function for the Theis solution (Appendix 1) has been plotted on graph paper. Compare this curve to our actual field (drawdown) data

See Figure 5.6 from Fetter, p. 170

- Shows W (u) vs. 1/u on log-log paper

A) Steps to a type curve solution:

1) Plot results from an aquifer test on graph paper. Use the same scale as the type curve plot.

Ask class: what would you plot?

See Figure 5.7 from Fetter, p. 171

- Plot drawdown (3 log cycles on y axis scale) vs. time (4 or 5 log cycles on x axis scale)

- Result should look similar to type curve

- Note: time is plotted in minutes here!

2) Overlay type curve and plot aquifer test results

- (light table or transparent type curve helps)

- Carefully slide type curve until it matches shape of pumping test

- Keep axes parallel (don't twist the type curve to make it match)

3) Pick a match point

- Match point is any intersecting line set on the overlay curve

- A common choice: point represented by W(u) = 1 and 1/u = 1

- Note: any match point should produce similar results

4) Read values for:

- W (u), 1/u, (ho - h) and t

- Often helpful to make a chart

5) Do necessary conversions (so that values from curve fit can be plugged into our altered version of Theis' equation)

- Convert 1/u to u

- Convert t from minutes to days (divide by 1440 min/day)

6) Plug values into Theis' rearranged equation to solve for T:

- Must know/be given a value for Q

- Convert discharge (Q) units to ft3/day if necessary

7) Plug values into Storativity equation to solve for storativity

- Use the value for T calculated above

S = 4 Ttu / r2

- Must be given a value for r (radial distance to an observation well)

- Note: you MUST have an observation well to calculate storativity using this method. Transmissivity (and hydraulic conductivity) can be calculated in a single well by observing the recovery curve when you turn the pump off. T and K can also be calculated using drawdown from an observation well.

8) Solve for K:

T = K b or K = T/b

- Do example in class: use 10/23 drawdown curve, Q = 42,000 ft3/d, r = 340 ft, b = 27 ft

- The result: we have determined T, K, S based on observed performance of the aquifer

- Now: will show two other graphical solutions to this problem: estimating aquifer parameters under non-equilibrium flow conditions

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